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Regression Theory for Near-Integrated Time Series

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  • Phillips, Peter C B

Abstract

The concept of a near-integrated vector random process is introduce d, helping the author work towards a general asymptotic theory of regression fo r multiple time series in which some series may be integrated processe s of the ARIMA type, others may be stable ARMA processes with near unit roots, and yet others may be mildly explosive. A limit theory for th e sample moments of such time series is developed using weak convergence. The theory is applied to the study of vector autoregress ions and cointegrating regressions of the type advanced by R. F. Engle and C. W. Granger (1987). A noncentral limiting distribution theory is derived for some recently-proposed multivariate unit root tests. Models with drift and near-integration are also studied. Copyright 1988 by The Econometric Society.

Suggested Citation

  • Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
  • Handle: RePEc:ecm:emetrp:v:56:y:1988:i:5:p:1021-43
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    References listed on IDEAS

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    1. Peter C.B. Phillips, 1986. "Weak Convergence to the Matrix Stochastic Integral BdB," Cowles Foundation Discussion Papers 796, Cowles Foundation for Research in Economics, Yale University.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    4. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    5. Phillips, P C B, 1974. "The Estimation of Some Continuous Time Models," Econometrica, Econometric Society, vol. 42(5), pages 803-823, September.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
    8. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
    9. Kramer, Walter, 1984. "On the consequences of trend for simultaneous equation estimation," Economics Letters, Elsevier, vol. 14(1), pages 23-30.
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